Global number field search results

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Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying matches 1-50 of 154)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.3243658447265625.1	x^16 - 5x^15 + 14x^14 - 30x^13 + 57x^12 - 100x^11 + 157x^10 - 215x^9 + 250x^8 - 240x^7 + 183x^6 - 110x^5 + 57x^4 - 30x^3 + 16x^2 - 5x + 1	\( 3^{12}\cdot 5^{14} \)	$C_8: C_2$ (as 16T6)	Trivial
16.0.18446744073709551616.6	x^16 - 8x^12 + 32x^8 + 8x^4 + 1	\( 2^{64} \)	$C_8: C_2$ (as 16T6)	Trivial
16.0.84480512701416015625.1	x^16 - 5x^15 + 21x^14 - 60x^13 + 167x^12 - 390x^11 + 863x^10 - 1665x^9 + 2915x^8 - 4545x^7 + 6502x^6 - 8600x^5 + 9652x^4 - 8300x^3 + 4994x^2 - 1900x + 361	\( 5^{14}\cdot 7^{12} \)	$C_8: C_2$ (as 16T6)	Trivial (GRH)
16.0.212576400000000000000.2	x^16 + 15x^14 + 135x^12 + 765x^10 + 2790x^8 + 6075x^6 + 7425x^4 + 4050x^2 + 2025	\( 2^{16}\cdot 3^{12}\cdot 5^{14} \)	$C_8: C_2$ (as 16T6)	$[2, 2]$
16.0.6710886400000000000000.1	x^16 + 16x^14 + 102x^12 - 40x^11 + 268x^10 - 260x^9 + 545x^8 - 560x^7 + 632x^6 - 980x^5 + 872x^4 - 480x^3 + 584x^2 - 660x + 241	\( 2^{40}\cdot 5^{14} \)	$C_8: C_2$ (as 16T6)	$[2]$
16.16.6710886400000000000000.1	x^16 - 4x^15 - 16x^14 + 76x^13 + 46x^12 - 392x^11 - 24x^10 + 928x^9 - 23x^8 - 1128x^7 - 44x^6 + 672x^5 + 96x^4 - 156x^3 - 36x^2 + 4x + 1	\( 2^{40}\cdot 5^{14} \)	$C_8: C_2$ (as 16T6)	Trivial (GRH)
16.0.54419558400000000000000.1	x^16 - 4x^15 + 30x^14 - 130x^13 + 480x^12 - 1062x^11 + 1758x^10 - 1790x^9 + 2070x^8 - 3150x^7 + 7638x^6 - 12792x^5 + 16655x^4 - 15200x^3 + 9870x^2 - 4374x + 1021	\( 2^{24}\cdot 3^{12}\cdot 5^{14} \)	$C_8: C_2$ (as 16T6)	$[2, 2, 2]$
16.16.54419558400000000000000.1	x^16 - 4x^15 - 30x^14 + 170x^13 - 30x^12 - 1002x^11 + 1038x^10 + 1840x^9 - 2280x^8 - 1770x^7 + 1908x^6 + 1068x^5 - 655x^4 - 350x^3 + 60x^2 + 36x + 1	\( 2^{24}\cdot 3^{12}\cdot 5^{14} \)	$C_8: C_2$ (as 16T6)	Trivial (GRH)
16.16.24031838291621636962890625.1	x^16 - 3x^15 - 39x^14 + 93x^13 + 411x^12 - 1084x^11 - 1181x^10 + 4319x^9 + 182x^8 - 6386x^7 + 2199x^6 + 3216x^5 - 1669x^4 - 132x^3 + 156x^2 - 23x + 1	\( 5^{14}\cdot 13^{14} \)	$C_8: C_2$ (as 16T6)	Trivial (GRH)
16.0.24031838291621636962890625.1	x^16 - 6x^15 + 39x^14 - 166x^13 + 531x^12 - 1408x^11 + 3521x^10 - 6688x^9 + 5707x^8 + 10008x^7 - 35249x^6 + 34498x^5 + 18416x^4 - 74104x^3 + 73424x^2 - 33984x + 15616	\( 5^{14}\cdot 13^{14} \)	$C_8: C_2$ (as 16T6)	$[5, 10]$ (GRH)
16.0.54498357372899208270500089.1	x^16 + 10x^14 - 31x^12 - 474x^10 - 700x^8 + 3681x^6 + 19433x^4 + 55682x^2 + 66049	\( 7^{12}\cdot 13^{14} \)	$C_8: C_2$ (as 16T6)	Trivial (GRH)
16.0.133756252636842779541015625.1	x^16 - 5x^15 - 21x^14 + 110x^13 + 182x^12 - 515x^11 + 1132x^10 + 7450x^9 + 6125x^8 - 55475x^7 - 145282x^6 + 16280x^5 + 430002x^4 + 532430x^3 + 278706x^2 + 67150x + 6241	\( 5^{14}\cdot 23^{12} \)	$C_8: C_2$ (as 16T6)	$[3]$ (GRH)
16.0.137350965859713069141239809.12	x^16 - 5x^15 + 6x^14 - 27x^13 + 25x^12 + 585x^11 - 11x^10 - 8941x^9 + 13194x^8 + 23931x^7 - 33867x^6 - 93236x^5 + 113868x^4 + 131958x^3 - 120127x^2 - 142546x + 125969	\( 13^{8}\cdot 17^{14} \)	$C_8: C_2$ (as 16T6)	$[2, 2, 2]$ (GRH)
16.0.158134644731459542671806121.1	x^16 - 5x^15 + 39x^14 - 206x^13 + 786x^12 - 2928x^11 + 9477x^10 - 24016x^9 + 52719x^8 - 106947x^7 + 186225x^6 - 291930x^5 + 417254x^4 - 465259x^3 + 404877x^2 - 251193x + 77917	\( 3^{12}\cdot 29^{14} \)	$C_8: C_2$ (as 16T6)	$[3]$ (GRH)
16.0.2859655432078149808865465089.5	x^16 - 4x^15 - 18x^14 + 140x^13 + 18x^12 - 1806x^11 + 3280x^10 + 9490x^9 - 35903x^8 - 10952x^7 + 320296x^6 - 908136x^5 + 1360137x^4 - 1288536x^3 + 1309611x^2 - 1608706x + 1191497	\( 17^{14}\cdot 19^{8} \)	$C_8: C_2$ (as 16T6)	$[104]$ (GRH)
16.0.12357173778709817574713851369.1	x^16 + 12x^14 - 54x^12 - 292x^10 - 3609x^8 - 11421x^6 + 169128x^4 + 702027x^2 + 531441	\( 11^{12}\cdot 13^{14} \)	$C_8: C_2$ (as 16T6)	$[5, 5, 5]$ (GRH)
16.16.14816104373013890157094140625.1	x^16 - 2x^15 - 44x^14 + 92x^13 + 711x^12 - 1546x^11 - 5220x^10 + 11797x^9 + 17566x^8 - 42194x^7 - 24745x^6 + 70914x^5 + 7866x^4 - 53147x^3 + 8714x^2 + 13605x - 4309	\( 5^{8}\cdot 41^{14} \)	$C_8: C_2$ (as 16T6)	Trivial (GRH)
16.0.243894230940323342291259765625.1	x^16 - 5x^15 - 46x^14 + 125x^13 + 1312x^12 + 1520x^11 - 16878x^10 - 77990x^9 + 115330x^8 + 973820x^7 - 2205112x^6 - 14067960x^5 + 11437842x^4 + 133312655x^3 + 206802536x^2 + 88567160x + 12313081	\( 5^{14}\cdot 43^{12} \)	$C_8: C_2$ (as 16T6)	$[7]$ (GRH)
16.0.709176532647391224615478515625.1	x^16 - 5x^15 - 54x^14 + 120x^13 + 2022x^12 + 2365x^11 - 37077x^10 - 93940x^9 + 252315x^8 + 476460x^7 + 397857x^6 + 15873125x^5 + 33865162x^4 - 62209555x^3 - 158984011x^2 + 96448345x + 272283001	\( 5^{14}\cdot 47^{12} \)	$C_8: C_2$ (as 16T6)	$[5]$ (GRH)
16.0.733360021453910541415126615929.1	x^16 - 6x^15 + 4x^14 + 48x^13 + 269x^12 + 1929x^11 + 3220x^10 - 14010x^9 + 4102x^8 + 418743x^7 + 1988414x^6 + 5468811x^5 + 10357688x^4 + 13227060x^3 + 10597823x^2 + 4677324x + 908209	\( 3^{12}\cdot 53^{14} \)	$C_8: C_2$ (as 16T6)	$[5]$ (GRH)
16.0.800737337114777368288115578449.1	x^16 - 3x^15 + 37x^14 - 250x^13 + 1434x^12 - 6102x^11 + 23233x^10 - 55975x^9 + 123893x^8 - 118276x^7 + 275740x^6 - 100624x^5 + 581200x^4 + 749376x^3 - 149248x^2 + 188416x + 262144	\( 3^{8}\cdot 73^{14} \)	$C_8: C_2$ (as 16T6)	$[4]$ (GRH)
16.0.1968033759133442969054057291329.5	x^16 - 4x^15 - 18x^14 + 4x^13 + 630x^12 - 854x^11 - 4132x^10 - 5402x^9 + 64057x^8 + 17336x^7 + 369868x^6 + 449552x^5 - 1606091x^4 - 4147460x^3 + 5655015x^2 + 18597494x + 16275257	\( 17^{14}\cdot 43^{8} \)	$C_8: C_2$ (as 16T6)	$[984]$ (GRH)
16.16.3922880935919264967742950184849.1	x^16 - x^15 - 85x^14 - 32x^13 + 2368x^12 + 3444x^11 - 23624x^10 - 51610x^9 + 68499x^8 + 210109x^7 - 39947x^6 - 325110x^5 - 71148x^4 + 189696x^3 + 70720x^2 - 33280x - 13312	\( 13^{12}\cdot 17^{14} \)	$C_8: C_2$ (as 16T6)	$[2]$ (GRH)
16.0.4009292695690170390860412175969.18	x^16 - 4x^15 + 50x^14 - 268x^13 + 1684x^12 - 8130x^11 + 35104x^10 - 143816x^9 + 508573x^8 - 1352592x^7 + 4667230x^6 - 6549280x^5 + 14771709x^4 - 16343158x^3 + 37249515x^2 - 2357794x + 47343743	\( 17^{14}\cdot 47^{8} \)	$C_8: C_2$ (as 16T6)	$[4, 4, 80]$ (GRH)
16.0.8714653896447035350446841659529.1	x^16 + 16x^14 - 460x^12 - 7651x^10 + 23792x^8 + 888119x^6 + 6440913x^4 + 19261746x^2 + 19280881	\( 13^{14}\cdot 19^{12} \)	$C_8: C_2$ (as 16T6)	$[3]$ (GRH)
16.0.9260065233133681348183837890625.1	x^16 - 3x^15 + 31x^14 - 82x^13 + 249x^12 + 323x^11 - 2638x^10 + 15109x^9 - 36239x^8 + 77070x^7 + 116867x^6 - 524611x^5 + 2609089x^4 - 6523510x^3 + 15629360x^2 - 21746376x + 15698896	\( 5^{12}\cdot 41^{14} \)	$C_8: C_2$ (as 16T6)	$[2, 50, 50]$ (GRH)
16.16.10483151353726139536553735554369.1	x^16 - 4x^15 - 86x^14 + 344x^13 + 2466x^12 - 9898x^11 - 27184x^10 + 109926x^9 + 120123x^8 - 491508x^7 - 131564x^6 + 706524x^5 - 328065x^4 - 12992x^3 + 22473x^2 - 676x - 169	\( 17^{14}\cdot 53^{8} \)	$C_8: C_2$ (as 16T6)	$[2]$ (GRH)
16.0.24722989956581301387479701814209.5	x^16 - 4x^15 + 50x^14 - 64x^13 + 1174x^12 - 786x^11 + 21844x^10 + 1738x^9 + 275707x^8 - 254052x^7 + 5039632x^6 - 12048508x^5 + 51842283x^4 - 82314412x^3 + 199952265x^2 - 187885492x + 289734503	\( 17^{14}\cdot 59^{8} \)	$C_8: C_2$ (as 16T6)	$[696]$ (GRH)
16.0.42832588164190465585875603485409.3	x^16 - x^15 + 43x^14 - 76x^13 + 1326x^12 - 2203x^11 + 21216x^10 - 30672x^9 + 236155x^8 - 184658x^7 + 823930x^6 + 1914443x^5 - 1141852x^4 + 6835864x^3 + 5582811x^2 - 3295057x + 16589329	\( 3^{8}\cdot 97^{14} \)	$C_8: C_2$ (as 16T6)	$[136]$ (GRH)
16.0.49943352689409528470220947265625.1	x^16 + 36x^14 - 2218x^12 - 56357x^10 + 1985485x^8 + 64738207x^6 + 610268042x^4 + 2074962124x^2 + 1335975601	\( 5^{14}\cdot 67^{12} \)	$C_8: C_2$ (as 16T6)	$[9]$ (GRH)
16.16.55005256933563283079156494140625.1	x^16 - 6x^15 - 104x^14 + 686x^13 + 3788x^12 - 30236x^11 - 46611x^10 + 627708x^9 - 315387x^8 - 5761286x^7 + 10976306x^6 + 12473518x^5 - 56521182x^4 + 58093288x^3 - 17141511x^2 - 4048152x + 1831516	\( 5^{14}\cdot 37^{14} \)	$C_8: C_2$ (as 16T6)	Trivial (GRH)
16.0.55005256933563283079156494140625.1	x^16 - 6x^15 + 81x^14 - 424x^13 + 2493x^12 - 9146x^11 + 40339x^10 - 111182x^9 + 226478x^8 + 508734x^7 - 2988049x^6 + 7062268x^5 + 7304373x^4 - 39342142x^3 + 86324549x^2 - 2254022x + 130734151	\( 5^{14}\cdot 37^{14} \)	$C_8: C_2$ (as 16T6)	$[13, 26]$ (GRH)
16.0.68372792983010839504523425519489.25	x^16 - 4x^15 - 86x^14 + 208x^13 + 3758x^12 - 4866x^11 - 91308x^10 + 39274x^9 + 1305907x^8 + 105532x^7 - 8912064x^6 + 5426132x^5 + 35639923x^4 - 98922188x^3 - 141482603x^2 + 495299900x + 784570571	\( 17^{14}\cdot 67^{8} \)	$C_8: C_2$ (as 16T6)	$[2, 2, 2, 4, 80]$ (GRH)
16.0.379236070824193420342929192569089.5	x^16 - 4x^15 - 86x^14 + 480x^13 + 2806x^12 - 22002x^11 - 24804x^10 + 474882x^9 - 616589x^8 - 3884708x^7 + 15339864x^6 - 31253884x^5 + 60004187x^4 - 42164356x^3 - 12439955x^2 - 321982852x + 779940859	\( 17^{14}\cdot 83^{8} \)	$C_8: C_2$ (as 16T6)	$[1272]$ (GRH)
16.0.652404832389289089417486572265625.1	x^16 - 5x^15 + 104x^14 - 90x^13 + 6012x^12 + 4535x^11 + 255252x^10 + 460820x^9 + 7746025x^8 + 22638150x^7 + 210234688x^6 + 641154675x^5 + 3240856012x^4 + 6091897560x^3 + 15754050266x^2 - 2417066385x + 276590161	\( 5^{14}\cdot 83^{12} \)	$C_8: C_2$ (as 16T6)	$[15]$ (GRH)
16.0.662834267162184237456650608633249.6	x^16 - 4x^15 + 118x^14 - 472x^13 + 5424x^12 - 20302x^11 + 128672x^10 - 406704x^9 + 1604631x^8 - 4306308x^7 + 11524894x^6 - 23360988x^5 + 42254283x^4 - 49841930x^3 + 55061061x^2 - 30043348x + 6029561	\( 17^{14}\cdot 89^{8} \)	$C_8: C_2$ (as 16T6)	$[2, 10, 10]$ (GRH)
16.0.764223041656422427087574156640625.5	x^16 - 6x^15 + 18x^14 + 48x^13 - 514x^12 + 2702x^11 - 4918x^10 + 890x^9 + 108574x^8 - 400144x^7 + 833586x^6 + 677858x^5 - 3244715x^4 + 7513276x^3 + 4757904x^2 + 102320x + 42852464	\( 5^{8}\cdot 89^{14} \)	$C_8: C_2$ (as 16T6)	$[65, 260]$ (GRH)
16.0.933865201156678930433597550025801.1	x^16 - x^15 - 88x^14 + 121x^13 + 3888x^12 - 2421x^11 - 93881x^10 - 85395x^9 + 1102409x^8 + 3857440x^7 + 7278998x^6 + 15382026x^5 + 37129668x^4 + 37380006x^3 + 32831156x^2 + 60659805x + 373271957	\( 11^{12}\cdot 29^{14} \)	$C_8: C_2$ (as 16T6)	$[5]$ (GRH)
16.0.2970275152580737243393920061992241.18	x^16 - 2x^15 + 12x^14 - 6x^13 + 253x^12 - 190x^11 + 10940x^10 - 42783x^9 + 111126x^8 + 250756x^7 + 592081x^6 - 7639120x^5 + 36803076x^4 - 51785747x^3 + 32623454x^2 + 119692325x + 51165007	\( 23^{8}\cdot 41^{14} \)	$C_8: C_2$ (as 16T6)	$[2, 4, 48]$ (GRH)
16.0.3101324844783200582771505158819929.1	x^16 + 22x^14 - 721x^12 + 11667x^10 + 520721x^8 - 383778x^6 - 29140165x^4 + 176923205x^2 + 343991209	\( 13^{14}\cdot 31^{12} \)	$C_8: C_2$ (as 16T6)	$[5, 15]$ (GRH)
16.0.8422523572126121633218804931640625.1	x^16 - 6x^15 + 109x^14 - 66x^13 + 1631x^12 + 18622x^11 + 23901x^10 + 278072x^9 + 1930997x^8 + 4400188x^7 + 16657011x^6 + 91551908x^5 + 279233036x^4 + 585873856x^3 + 836081984x^2 + 529353216x + 157623296	\( 5^{14}\cdot 53^{14} \)	$C_8: C_2$ (as 16T6)	$[53, 106]$ (GRH)
16.16.8422523572126121633218804931640625.1	x^16 - 6x^15 - 156x^14 + 464x^13 + 9846x^12 + 602x^11 - 274489x^10 - 670628x^9 + 2257212x^8 + 12490108x^7 + 16208101x^6 - 10828192x^5 - 42119744x^4 - 23145964x^3 + 12749774x^2 + 9245136x - 1985409	\( 5^{14}\cdot 53^{14} \)	$C_8: C_2$ (as 16T6)	Trivial (GRH)
16.0.32349497931606921267167334562710001.18	x^16 - 4x^15 - 54x^14 + 432x^13 + 674x^12 - 17034x^11 + 49248x^10 + 192390x^9 - 1631495x^8 + 2807348x^7 + 14973336x^6 - 110186296x^5 + 363624245x^4 - 759633956x^3 + 1071727507x^2 - 977305750x + 484313617	\( 31^{8}\cdot 41^{14} \)	$C_8: C_2$ (as 16T6)	$[2, 2, 120]$ (GRH)
16.16.133225631225242544609121034154723281.1	x^16 - 2x^15 - 190x^14 + 450x^13 + 12853x^12 - 32724x^11 - 380372x^10 + 877563x^9 + 5254594x^8 - 7678424x^7 - 36909197x^6 + 10490174x^5 + 101413382x^4 + 62563841x^3 - 14494532x^2 - 14116519x - 2033869	\( 37^{8}\cdot 41^{14} \)	$C_8: C_2$ (as 16T6)	Trivial (GRH)
16.0.136708075730434417658369530269167641.1	x^16 - 5x^15 + 92x^14 - 995x^13 + 6157x^12 - 49434x^11 + 287286x^10 - 599430x^9 + 8227470x^8 + 1047639x^7 + 107694699x^6 + 24673950x^5 + 696973786x^4 + 190246216x^3 + 1566061688x^2 + 738777220x + 87593557	\( 7^{12}\cdot 61^{14} \)	$C_8: C_2$ (as 16T6)	$[5]$ (GRH)
16.0.419374069872350970710519002168327921.4	x^16 - 2x^15 - 54x^14 - 454x^13 - 207x^12 + 16650x^11 + 145223x^10 + 735470x^9 + 2751785x^8 + 7653230x^7 + 16017095x^6 + 26533814x^5 + 41196780x^4 + 54084660x^3 + 40870017x^2 - 5449640x + 2688284	\( 11^{8}\cdot 89^{14} \)	$C_8: C_2$ (as 16T6)	$[2, 2, 8]$ (GRH)
16.0.443324403828803432927172239238695761.5	x^16 - 2x^15 - 30x^14 + 170x^13 + 493x^12 - 3932x^11 + 151484x^10 - 772973x^9 + 5788342x^8 - 18480176x^7 + 108110739x^6 - 141573402x^5 + 995637614x^4 - 80045271x^3 + 5798763048x^2 + 1158532737x + 10143812191	\( 41^{14}\cdot 43^{8} \)	$C_8: C_2$ (as 16T6)	$[1740]$ (GRH)
16.0.457489601812551940177211781114570649.1	x^16 + 30x^14 - 2853x^12 - 77889x^10 + 2774661x^8 + 101508906x^6 + 835715203x^4 + 2304643077x^2 + 749062161	\( 13^{14}\cdot 47^{12} \)	$C_8: C_2$ (as 16T6)	$[5, 5]$ (GRH)
16.16.477639401035264016929733847900390625.1	x^16 - x^15 - 161x^14 + 89x^13 + 10289x^12 + 226x^11 - 336497x^10 - 234933x^9 + 5957206x^8 + 8516080x^7 - 52900437x^6 - 119238518x^5 + 154809239x^4 + 611877670x^3 + 359251250x^2 - 256164513x - 219439429	\( 5^{12}\cdot 89^{14} \)	$C_8: C_2$ (as 16T6)	$[4]$ (GRH)
16.0.658590075672306993006756541342366441.1	x^16 + 24x^14 - 1024x^12 - 28619x^10 + 175088x^8 + 9841099x^6 + 91602093x^4 + 300750338x^2 + 214651801	\( 19^{12}\cdot 29^{14} \)	$C_8: C_2$ (as 16T6)	$[5, 5, 65]$ (GRH)